There are efficient and convergent interior point methods to solve linearly and nonlinearly constrained problems, one of these procedures being Vanderbei and Shanno's method. A simplification of it, here denoted the "naive" method, to solve linearly and nonlinearly constrained quadratic problems will be described, and also a restricted-step variant of it. Both procedures were implemented and tested on several realistic cases of short-term electric generation scheduling for problem sizes up to 13000 variables.
A convergence analysis is presented for the "naive" method. It is shown that nonlinear primal infeasibility and dual infeasibility at each iteration are bounded above by a quadratic with respect to step size, whereas primal and dual infeasibility decrease linearly for linearly constrained quadratic programming. The parameters of the quadratic bound in nonlinear primal and dual infeasibilities are related with the curvature of the nonlinear constraints. Computational tests performed conform to the theoretical developments described.
Numerical instability appears in the solution of some cases and it affects convergence. A numerical exemple is presented and the reasons for it are examined.
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